Sure, smaller warheads every couple square miles would be worse, but I was talking about your original scenario as described. Also, looking at it more carefully your initial numbers started off wrong by a factor of 4.
There are about 200 million square miles of land area. If you cut that in half (for mountains and deserts, which means the people already living in those places are left completely fine by the initial blasts), that's still half the density you started with.
At 166 square miles, Barbados would get one nuke. NUKEMAP calculates
that an airburst over the center of the island would kill 33,705 people, injure another 113k, and leave the remaining 140k residents unhurt. (These numbers could of course be altered significantly by taking population distribution into account when deciding where precisely to detonate, but adjusting for population density wasn't part of your original scenario.)
? Not by a long shot.
A long shot, but not *such* a long shot.
According to several sources, 200,000,000sq miles appears to be *total surface area* (196,940,000sq miles).
I went straight to the wiki for Earth and rounded the figure for land area (57,510,000sq miles) to 50mil. The figure for inhabitable area I found somewhere else and similarly rounded it to 25mil.
Given the coverage and resilience of things like bacteria, and since I am ignoring the sea (so the land could be re-innoculated at any time with at least *something*) perhaps total sterility is not literally possible, no, but I think that the sheer amount of residual radiation would give it a good ol'British try!
NB: Of course, the closer you look (eg: Barbados) the more likely the gross assumptions would break down. Plus if one was really serious, of course you wouldn't evenly spread the weapons, you'd be more picky. The model, like most, is illustrative only. On the other hand, smaller warheads are not only worse but allow a greater resolution. Barbados may only receive 1 (or 2, if you round up) weapon in the 1MT model, but in the 20kt model it would receive 83!
Anyhoo, thats with only 10kg AM. Gimme a ton and we'll talk again about your precious "bacteria".
"Civilisation ending" - If this is all you want to achieve I think it could be done with *significantly* less destruction, since people will finish the job themselves if you remove enough infrastructure. All you need is a decent WWIII-scale scenario. Put a few large dirty bursts in the most fertile areas to seal the deal.
I wonder if another approach might be worth a look-
Use your 10kg AM as before to create 470-odd gigatons of AM-catalysed H-bombs, and use these to vaporise as much seawater as possible, with the aim of causing a runaway greenhouse effect. I have no idea if this is a workable quantity of water vapour for this purpose, but it seems like quite a lot of bang-for-the-buck in terms of atmospheric engineering with 10kg AM.
Rough calcs -
1ton TNT = 4.184GJ
Energy to boil 1L water, starting somewhere between 0-10degC, 1atm. = ~2600kJ/L
1ton TNT boils ~ 1600L water
473Gigatons TNT boils ~ 7.57e14kg water
Current atmosphere approx 0.4% water vapour
Mass of atmosphere ~5.15e18kg
Of which water vapour = 2e16kg
473Gigatons of boiled water will only net you a few percent increase in water vapour globally. Probably less. Is this enough to spark major changes?
Or would the dust raised from land-based detonations be a larger concern?